.. _gwpy-example-frequencyseries-rayleigh: .. sectionauthor:: Duncan Macleod .. currentmodule:: gwpy.frequencyseries Plotting a Rayleigh-statistic `Spectrum` ######################################## In LIGO the 'Rayleigh' statistic is a calculation of the `coefficient of variation `_ of the power spectral density (PSD) of a given set of data. It is used to measure the 'Gaussianity' of those data, where a value of 1 indicates Gaussian behaviour, less than 1 indicates coherent variations, and greater than 1 indicates incoherent variation. It is a useful measure of the quality of the strain data being generated and recorded at a LIGO site. To demonstate this, we can load some data from the LIGO Livingston intereferometer around the time of the GW151226 gravitational wave detection: .. plot:: :nofigs: :include-source: :context: reset from gwpy.timeseries import TimeSeries gwdata = TimeSeries.fetch_open_data('L1', 'Dec 26 2015 03:37', 'Dec 26 2015 03:47', verbose=True) Next, we can calculate a Rayleigh statistic `FrequencySeries` using the :meth:`~gwpy.timeseries.TimeSeries.rayleigh_spectrum` method of the `~gwpy.timeseries.TimeSeries` with a 2-second FFT and 1-second overlap (50%): .. plot:: :nofigs: :include-source: :context: rayleigh = gwdata.rayleigh_spectrum(2, 1) For easy comparison, we can calculate the spectral sensitivity ASD of the strain data and plot both on the same figure: .. plot:: :include-source: :context: asd = gwdata.asd(2, 1) plot = asd.plot(figsize=(8, 6)) plot.add_frequencyseries(rayleigh, newax=True, sharex=plot.axes[0]) asdax, rayax = plot.axes asdax.set_xlabel('') asdax.set_xlim(30, 1500) asdax.set_ylim(5e-24, 1e-21) asdax.set_ylabel(r'[strain/\rtHz]') rayax.set_ylim(0, 2) rayax.set_ylabel('Rayleigh statistic') asdax.set_title('Sensitivity of LIGO-Livingston around GW151226', fontsize=20) plot.show() So, we see sharp dips at certain frequencies associated with 'lines' in spectrum where noise at a fixed frequency is very coherent (e.g. harmonics of the 60Hz mains power supply), and bumps in specific frequency bands where the interferometer noise is non-stationary.